Second Week Final Test

\frac{a}{b}

a/b

Correct

Correct!

6

6

Correct

Correct!

Question 3

Fill all the gaps in the sentences with o (write "small" in the answer without o), O (write "big" in the answer without o) or numbers in order to make correct statements: "By the definition of the big-O and little-o, one should assume, that if $f=$ ***** $(g)$ then $f=$ ***** $(g)$ . Take, for instance, functions $f(x)=\sin x$ and $g(x)=x$ as $x \to +\infty$ . Since $\sin {x} / x \to$ *****, then $f=$ ***** $(g)$ ; but, in the same time $|\sin{x}|\le 1\cdot |x|$ , then $f=$ ***** $(g)$ ."

Write answers in the order of gaps; separate by semi-colons.

1 / 1 point

small;big;0;small;big

Correct

the limit of the function of two variables could be found by consequential taking limits by each of its variables

Correct

That's it

levels of the multivariate function could look like straight lines intersecting at $(0,0)$ if for each of them $(0,0)$ point is excluded from the level

it is possible to fully reconstruct the function just by shapes of its levels (without knowledge of the values at this levels)

Correct

Compare $f(x,y)=x^2+y^2$ and $f(x,y)=\sqrt{x^2+y^2}$

if some point $M$ of the real plain does not belong to any level of the function $f$ , then this point is not included into the functions domain either

1

Correct

Correct!

2

3

Correct

Correct!

-1000

-1000

Correct

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